Abstract
I suggest that QCD perturbation theory can be convergent, and that “optimization” of the renormalization scheme choice is essential in achieving this. Arguing that higher orders probe shorter distances, I suggest that the effective expansion parameter (the “optimized” couplant) decreases at high orders, leading to an induced convergence. The mechanism is illustrated by a simple mathematical example. The point is that, even if the perturbation series is divergent in all fixed renormalization schemes, the sequence of “optimized” approximations may still converge. It is emphasized that the limit approached by perturbation theory, if any, will not be the exact result of the full theory. Allegations that QCD series are not Borel-summable are critically re-examined in this light.
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